Let $W_{m,n}^+$ be the Lie superalgebra of vector fields on ${\mathbb C}^{m|n}$. In this talk, we will give a survey of various applications of $A$-cover method developed by Y. Billig and V.

Futorny, and introduce the known results on tensor modules by various researchers. Based on the important work by D. Grantcharov and V. Serganova on the classification of simple finite modules over the Lie algebra of polynomial vector fields, we will show that any strong finite $W_{m,n}^+$ module is also a tensor module. This talk is based on a joint work with Y. Cai and Y. Xue.